Heckscher-Ohlin and the ‘principle of explosion’

The other day yours truly had a post up on the Heckscher-Ohlin theorem, arguing that since the assumptions on which the theorem build are empirically false, one might, from a methodological point of view, wonder

how we are supposed to evaluate tests of a theorem building on known to be false assumptions. What is the point of such tests? What can those tests possibly teach us? From falsehoods anything logically follows.

Some people have had troubles with the last sentence — from falsehoods anything whatsoever follows.

But that’s really nothing very deep or controversial. What I’m referring to — without going into the intricacies of distinguishing between ‘false,’ ‘inconsistent’ and ‘self-contradictory’ statements — is the well-known ‘principle of explosion,’ according to which if both a statement and its negation are considered true, any statement whatsoever can be inferred.

Whilst tautologies, purely existential statements and other nonfalsiﬁable statements assert, as it were, too little about the class of possible basic statements, self-contradictory statements assert too much. From a self-contradictory statement, any statement whatsoever can be validly deduced. Consequently, the class of its potential falsiﬁers is identical with that of all possible basic statements: it is falsiﬁed by any statement whatsoever.

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I guess I am one of those some people who have trouble with the statement “From falsehoods anything logically follows”, particularly if it is used in the context of empirical errors.

I will try to explain again what I mean:

There is a clear distinction between “false” on the one hand and “inconsistent” or “self-contradictory” on the other. And that should not be controversial because it is an elementary logical distinction.

Let me explain further:

Let us say I make the assumption that x is true. And from x follows y. Therefore I can deduce (under the assumption that x is true) that y is true.
[A]: x.
x AND (x => y) => y.

Let us say that in reality x is never true.
[R]: ¬x.
Then, because x is false, even though from x follows y, we cannot say whether y is true or not.
¬x AND (x => y) => y OR ¬y.

In this case [A] is a false assumption. [A] and [R] are incompatible.

But that assumption [A] is *not* contradictory because it only states that x is true, it does *not* at the same time state that x is false.

Therefore one *cannot* apply the principle of explosion to that statement.

From a contrafactual assumption like [A] other statements *can* be deduced logically correctly. It is just that those deduced statement are not valid in the real world because in the real world the assumptions are not given.

Because of this fundamental difference between
— false assumption (empirical error) and
— contradiction (logical error)
the correct formulation for the principle of explosion is
“ex *contradictione* sequitur quolibet”
while the other formulation
“ex falso sequitur quodlibet”
is imprecise and mistakable.

Now: All ‘utility’ is subjective satisfaction with and Not all ‘utility’ is subjective satisfaction with. [I.e., Where it is not subjective satisfaction with, it is an objective benefit that follows from.]

With these statements, anything can be proved.

What is more likely is that satisfaction with is a function of benefits from, though that is not the complete story.

Or,

All ‘economic values’ are only monetary exchange-value between commodities and Not all ‘economic values’ are monetary exchange-value between commodities: I.e., these are distinguishable, separable, and objective values-in-uses.

The former statement implies substitution rates between commodities based solely upon there exchange values/price relations.

The latter implies that some goods may be substitutes for some end uses but and also that any substitution between commodities is a function of the properties of commodities and not simply of price relationships. And, this means that it will be the case that prices may affect commodity substitution only where such substitution in terms of values-in-use can occur.

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